Fixed length line between moving points along circles

Hi All,

I am new to Rhino, Grasshopper and this forum - my background is about 10 years of SolidWorks ( I guess I have seen the light).

I'm trying to move a fixed length line along two circles. 

The jpeg shows the desired start and end positions. (the first circle lives in the yz plane, the other in the xz plane. 

The attached grasshopper file is a stripped down version - 

I have thus far tried dividing the circles and creating a line between the end points - controlled via a single slider. This works, however the length of the line changes because the angle relationship is not equal. 

Can anyone give me direction on the math needed to calculate this relationship or is there a way to set the length of the line as well as the start and end points (I believe this would have two solutions?). 

Thanks